advances.sciencemag.org/cgi/content/full/6/23/eaba0504/DC1

Supplementary Materials for

The robustness of reciprocity: Experimental evidence that each form of reciprocity

is robust to the presence of other forms of reciprocity

David Melamed*, Brent Simpson*, Jered Abernathy

*Corresponding author. Email: melamed.9@osu.edu (D.M.); bts@mailbox.sc.edu (B.S.)

Published 3 June 2020, Sci. Adv. 6, eaba0504 (2020)

DOI: 10.1126/sciadv.aba0504

This PDF file includes:

Sections S1 and S2 Tables S1 to S5

1 Experimental Details

The experiment, briefly described in the main text, was conducted using Workers from

Amazon’s Mechanical Turk. During the Spring of 2018, research assistants posted a HIT to

Amazon for the study. After accepting the HIT, Workers followed a link to a Qualtrics survey.

They first read detailed instructions. Then they completed comprehension check items to ensure

that they understood the instructions. Next Qualtrics randomly selected 6 of the 81 conditions for

the participant to complete. Finally, participants filled out a questionnaire that included their

demographic information and gave them an opportunity to make qualitative comments about the

study. Below are screenshots from the survey.

Selected Screenshots

Study Instructions

Comprehension Checks

[Condition 1: Control]

[Direct Reciprocity Condition 2]

[Direct Reciprocity Condition 3]

[Generalized Reciprocity Condition 2]

[Reputational Giving Condition 2]

[Rewarding Reciprocity Condition 2]

[Combined Condition 3 for all four types of reciprocity]

2 Statistical Analyses

Descriptive statistics for the participants’ prosocial behaviors are reported in Table S1.

We caution readers about interpreting Table S1, however, because in both generalized

reciprocity and rewarding reciprocity conditions others gave randomized amounts and those are

not controlled in the table. The amounts given by the simulated others have a significant impact

on participant giving (see below).

Table S1: Summaries of how much participants gave in the various conditions.

Direct Reciprocity

Control

Direct Reciprocity First

Mover

Direct Reciprocity

Second Mover

N Mean St.

Dev.

N Mean St.

Dev.

N Mean St.

Dev.

GR=0;RG=0;RR=0 50 4.94 3.61 54 5.63 3.01 56 4.63 3.40

GR=1;RG=0;RR=0 55 4.58 3.35 56 5.38 3.15 51 5.29 3.41

GR=2;RG=0;RR=0 58 5.21 2.94 52 6.27 3.09 48 4.60 3.13

GR=0;RG=1;RR=0 53 6.04 2.62 50 6.12 2.98 54 5.11 3.10

GR=1;RG=1;RR=0 47 5.13 2.50 52 5.65 3.23 54 5.20 2.80

GR=2;RG=1;RR=0 53 4.43 3.41 55 5.82 3.17 54 3.44 3.49

GR=0;RG=2;RR=0 56 5.69 2.76 49 6.08 3.03 57 5.53 3.12

GR=1;RG=2;RR=0 52 5.75 2.81 53 6.38 2.83 47 4.87 3.23

GR=2;RG=2;RR=0 50 4.38 3.36 53 5.66 2.95 51 4.29 3.36

GR=0;RG=0;RR=1 52 4.31 3.13 53 5.25 3.32 51 4.10 3.31

GR=1;RG=0;RR=1 55 3.89 3.18 51 5.04 2.99 52 4.83 3.31

GR=2;RG=0;RR=1 51 4.75 2.50 50 5.38 2.81 53 4.77 3.01

GR=0;RG=1;RR=1 53 5.09 3.17 49 4.98 3.02 53 5.40 3.32

GR=1;RG=1;RR=1 54 4.59 3.41 53 5.00 3.15 55 5.25 3.02

GR=2;RG=1;RR=1 50 5.16 3.63 53 5.26 2.88 52 6.27 3.24

GR=0;RG=2;RR=1 45 4.67 3.19 56 5.71 3.28 49 5.04 3.59

GR=1;RG=2;RR=1 56 4.77 2.98 55 5.04 3.06 51 5.16 3.31

GR=2;RG=2;RR=1 53 4.75 3.31 53 5.77 2.71 57 5.56 3.16

GR=0;RG=0;RR=2 58 5.21 2.94 52 6.27 3.09 48 4.60 3.13

GR=1;RG=0;RR=2 53 4.43 3.41 55 5.82 3.17 54 3.44 3.49

GR=2;RG=0;RR=2 56 4.91 2.83 50 5.80 3.65 50 5.36 3.19

GR=0;RG=1;RR=2 51 4.75 2.50 50 5.38 2.81 53 4.77 3.01

GR=1;RG=1;RR=2 50 5.16 3.63 53 5.26 2.88 52 6.27 3.24

GR=2;RG=1;RR=2 55 4.78 3.08 52 5.67 3.04 51 5.88 3.17

GR=0;RG=2;RR=2 56 4.91 2.83 50 5.80 3.65 50 5.36 3.19

GR=1;RG=2;RR=2 55 4.78 3.08 52 5.67 3.04 51 5.88 3.16

GR=2;RG=2;RR=2 51 5.43 3.21 55 6.18 3.26 50 5.42 3.30

Note: For Generalized Reciprocity (GR): 0 = the control condition, 1 = Received from one other,

2 = Received from two others. For Reputational Giving (RG): 0 = the control condition, 1 = one

observer of the participant’s giving who will give to them subsequently, 2 = two observers of the

participant’s giving who will give to them subsequently. For Rewarding Reciprocity (RR): 0 =

the control condition, 1 = the alter gave to one other before the participant gives, 2 = the alter

gave to two others before the participant gives.

In terms of modeling prosocial giving, we estimated linear mixed models, with multiple

decisions nested in each participant. Model 1 in Table S2 can be written more formally as

follows:

(𝑃𝑜𝑖𝑛𝑡𝑠 𝐺𝑖𝑣𝑒𝑛) = 𝛽0 + 𝛽1(𝐷𝑅 𝐹𝑖𝑟𝑠𝑡 − 𝑀𝑜𝑣𝑒𝑟)𝑝 +

∑ 𝛽(𝑞+1)(𝐶𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛)6

𝑞=1+ 𝛽8(𝑀𝑎𝑙𝑒) + 𝜋0𝑝

Where: 𝛽0 refers to the intercept; 𝛽1 refers to the effect of being in the condition where the

participant gives to another and that other will reciprocate the participant’s giving; Q refers to a

series of dummy variables for the conditions in the other forms of reciprocity (GR 1 Other, GR 2

Others, RR 1 Other, RR 2 Others, IR 1 Other, IR 2 Others); 𝛽q refers to the linear effect of the qth

dummy variable; 𝛽8 refers to the linear effect of male participants; 𝜋0𝑝 refers to the variance

component on the intercept corresponding to conditions in participants; subscript p refers to

something that varies within participants; and we assume, 𝜋0𝑝 ~ iid N(0, 𝜎2 ). Parameter

estimated were obtained using Maximum Likelihood Estimation. Our other models of points

given were similarly specified and estimated.

Table S2 presents our Direct Reciprocity results. Model 1 shows that when the participant

is giving to someone that will have an opportunity to give back to them, they give them an

additional .507 points compared to the baseline condition. This is net of a series of dummy

variables for the conditions for the other forms of reciprocity. Model 2 shows how participants

responded to be the second mover in a Direct Reciprocity relation (i.e., someone gave to the

participant, and the participant is giving back) compared to the baseline. Here we find that being

in this condition has a negative effect compared to the baseline, and that there is a positive effect

of how much the other gave to the participant. This effect is illustrated in Figure 1, and holds net

of the same controls as in Model 1. We tested for interactions to see whether the other forms of

reciprocity moderate the effects of DR on giving. In particular, we began by specifying two-way

interactions between our terms for DR, and the other forms of reciprocity. We then constrained

the interaction with the smallest t-value and estimated tests of nested models using Likelihood

Ratio tests for nested models. For both specifications of Direct Reciprocity, we were able to

constrain all of the interaction effects, meaning that the effect of DR is not contingent on the

presence of other bases of reciprocity.

Table S2: Direct reciprocity results from linear mixed models predicting giving.

Model 1 Model 2

DR First Mover 0.507***

(0.088)

DR Second Mover

-1.502***

(0.136)

Points Given by Alter

0.339***

(0.021)

GR 1 Other -0.187

(0.108)

-0.081

(0.110)

GR 2 Others -0.093

(0.108)

0.171

(0.109)

RR 1 Other -0.539***

(0.108)

-0.343***

(0.110)

RR 2 Others -0.192

(0.107)

-0.169

(0.110)

RG 1 Other 0.192

(0.108)

0.572***

(0.108)

RG 2 Others 0.368***

(0.107)

0.667***

(0.110)

Male -0.289

(0.195)

-0.564**

(0.193)

Constant 5.160***

(0.151)

4.744***

(0.154)

Variance Component 5.178***

(0.341)

5.037***

(0.333)

Note: *p < .05, **p < .01, and ***p < .001. N = 2,741 participant-trials.

Table S3 presents our results for the Generalized Reciprocity conditions. Model 1

includes a term “Other Gave” which refers to the number of points that the simulated others gave

to the participants before the participant decided how many points to give to someone else. When

there were two simulated others that gave to the participant, we averaged them in Models 1 and

2. [Trying to estimate the effect of giving on the part of both simulated others results in

significant missing data patterns (e.g., when only one person gave to the participant, there is

missing data for the second giver).] Model 1 shows that for each point the participant received,

they paid it forward by .132 to someone else. This holds net of dummy variables for the other

bases of reciprocity. We also checked whether the other forms of reciprocity moderated the

effect of GR on giving. We used the same procedure for tests of nested models that we used for

Direct Reciprocity. Here we found that rewarding reputations moderates the effect of

Generalized Reciprocity (Figure 2). In particular, when rewarding reputations is absent,

Generalized Reciprocity has the strongest effect. Model 3 assesses diminishing marginal effects

of there being multiple others giving to the participant. In Model 3, “Other gave” is the total

points given to the participant before he or she decides how many points to give to someone else.

This is in contrast to Models 1 and 2, where the term is total points in conditions where one other

gave to the participant, and the average given for both others in conditions where two others

gave to the participant. In addition to this difference, Model 3 also includes a dummy variable for

whether there were two others giving to the participant, and an interaction effect between this

dummy variable and “Other gave.” The interaction effect tells us if the effect of “Other gave”

varies by how many others were present. We find that the interaction effect is not significant,

indicating that there is no evidence for a diminishing effect of generalized reciprocity: the more

points participants receive (regardless of how many people are giving to them), the more they

pay forward. Model 4 makes a similar point. Here we include “Other gave” as the sum of the

points the participant received (same as Model 3), and a squared term. While the squared term

approaches significance (p = .073), it is not significant, meaning that points received are paid

forward without diminishing returns.

Table S3: Generalized reciprocity results from linear mixed models predicting giving.

Model 1 Model 2 Model 3 Model 4

Other Gave (GR) 0.132***

(0.022)

0.224***

(0.038)

.112***

(.026)

.143***

(.041)

RR 1 Other (RR1) -0.316*

(0.145)

0.259

(0.308)

-.321*

(.145)

-.313*

(.145)

RR 2 Others (RR2) -0.093

(0.148)

0.717*

(0.307)

-.096

(.147)

.109

(.148)

RG 1 Other 0.516***

(0.146)

0.510***

(0.145)

.522***

(.145)

.521***

(.146)

RG 2 Others 0.637***

(0.145)

0.647***

(0.145)

.643***

(.145)

.636***

(.145)

DR First Mover (DR1) 0.759***

(0.167)

0.771***

(0.166)

.763***

(.167)

.745***

(.167)

DR Second Mover (DR2) 0.439**

(0.155)

0.426**

(0.154)

.442**

(.155)

.424**

(.155)

GR x RR1

-0.113*

(0.053)

GR x RR2

-0.160**

(0.053)

Two Others Present to GR

(T)

-.189

(.265)

GR x T

-.026

(.032)

GR^2

-.004

(.0023)

Male -0.663**

(0.224)

-0.659**

(0.224)

-.660**

(.224)

-.660**

(.225)

Constant 3.871***

(0.232)

3.403***

(0.280)

3.908***

(.248)

3.795***

(.252)

Variance Component 5.404***

(0.422)

5.418***

(0.422)

5.410***

(.423)

5.420***

(.424)

Note: *p < .05, **p < .01, and ***p < .001. N = 4,254 participant-trials.

Table S4 presents our results for reputational giving. The presence of others to indirectly

reciprocate the participant’s giving indeed increases how much participants give. This holds net

of controls for the other forms of giving. We do find, however, evidence that the effect of

reputational giving is moderated by direct reciprocity. As illustrated in Figure 3, reputational

giving has the largest effect in the absence of direct reciprocity, but it still has a positive effect on

giving even in the presence of direct reciprocity.

Table S4: Reputational Giving results from linear mixed models predicting giving.

Model 1 Model 2

RG 1 Other (RG1) 0.405***

(0.090)

0.359*

(0.155)

RG 2 Others (RG2) 0.521***

(.090)

0.528***

(0.155)

GR 1 Other -0.111

(0.090)

-0.108

(0.090)

GR 2 Others 0.013

(0.090)

0.017

(0.090)

RR 1 Other -0.416***

(0.090)

-0.415***

(0.090)

RR 2 Others

-0.146

(0.090)

-0.148

(0.090)

DR First Mover (DR1) 0.521***

(0.090)

0.742***

(0.155)

DR Second Mover (DR2) 0.184*

(0.090)

-0.073

(0.155)

RG1 x DR1

-0.349

(0.219)

RG1 x DR2

0.478*

(0.220)

RG2 x DR1

-0.312

(0.219)

RG2 x DR2

0.302

(0.222)

Male -0.440*

(0.186)

-0.441*

(0.186)

Constant 4.931***

(0.139)

4.939***

(0.157)

Variance Component 4.989***

(0.309)

4.994***

(0.310)

Note: *p < .05, **p < .01, and ***p < .001. N = 4,254 participant-trials.

Finally, Table S5 presents our results for rewarding reputations. We model this as a

continuous variable corresponding to the number of points that alter gave to someone else before

the participant decides how much to give to alter. As with generalized reciprocity, when alter

gave points to two others, we average the number of points they gave (Models 1 and 2). Net of

the other bases of reciprocity, we find that participants give more to others, the more they have

already given. We also find that the effect of rewarding reputations is moderated by direct

reciprocity. As illustrated in Figure 4, participants reward giving unless the person to whom they

are giving has given to directly to them. In this case, participants are only attuned to how much

they received from the alter, rather than how much alter gave to others. Model 3 assesses

diminishing marginal effects of the other to whom the participant is giving having already given

to multiple others. In Model 3, “Alter gave Other” is the total points alter gave to others before

the participant decides how many points to give alter. This is in contrast to Models 1 and 2,

where the term is total points in conditions where alter gave to one other, and the average given

to both others in conditions where alter gave to two others. In addition to this difference, Model

3 also includes a dummy variable for whether alter gave to two others, and an interaction effect

between this dummy variable and “Alter gave Other.” The interaction effect tells us if the effect

of “Alter gave to Other” varies by how many others were present. We find that the interaction

effect is not significant, indicating that there is no evidence for a diminishing effect of rewarding

reciprocity: the more points alter gave to others, the more the participant gives alter. Similarly

Model 4 includes a squared-term for “Alter gave Other.” Again we find no evidence of

diminishing returns: the more points alter gave to others, the more the participant rewards them.

Table S5: Rewarding reputations results from linear mixed models predicting giving.

Model 1 Model 2 Model 3 Model 4

Alter gave Other (RR) 0.175***

(0.022)

0.333***

(0.040)

.158***

(.026)

.175***

(.041)

GR 1 Other -0.020

(0.143)

-0.061

(0.142)

-.029

(.143)

-.043

(.143)

GR 2 Others 0.044

(0.144)

0.027

(0.143)

.026

(.144)

.003

(.144)

RG 1 Other 0.493***

(0.145)

0.528***

(0.143)

.491**

(.144)

.488**

(.145)

RG 2 Others 0.673***

(0.145)

0.705***

(0.143)

.672***

(.144)

.663***

(.145)

DR First Mover (DR1) 0.661***

(0.165)

0.837*

(0.332)

.658***

(.165)

.646***

(.165)

DR Second Mover (DR2) 0.375*

(0.146)

1.878***

(0.282)

.362*

(.146)

.336*

(.146)

RR x DR1

-0.041

(0.059)

RR x DR2

-0.307***

(0.050)

Alter gave to Two Other

(T)

-.042

(.260)

RR x T

-.053

(.032)

RR^2

-.004

(.0024)

Male -0.524*

(0.219)

-0.572**

(0.217)

-.526*

(.219)

-.526*

(.219)

Constant 3.479***

(0.214)

2.720***

(0.268)

3.479***

(.227)

3.459***

(.232)

Variance Component 5.100***

(0.401)

5.014***

(0.394)

5.116***

(.402)

5.124***

(.402)

Note: *p < .05, **p < .01, and ***p < .001. N = 4,254 participant-trials.